From Monte Carlo to quantum computation

Mathematics and Computers in Simulation

Volumn 62, Issue 3-6, 2003, Pages 219-230

  Heinrich, Stefan ^a  

^a Rheinland Pfälzische Technische Universität Kaiserslautern Landau   (Germany)

Author keywords

Monte Carlo algorithms; Quantum computation complexity

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; COMPUTER SIMULATION; INTEGRATION; MONTE CARLO METHODS; PROBLEM SOLVING; RANDOM PROCESSES;

QUANTUM COMPUTATION COMPLEXITY;

QUANTUM THEORY;

EID: 0037417056     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-4754(02)00239-2     Document Type: Conference Paper

References (28)

1. D. Aharonov, Quantum computation - a review, in: Annual Review of Computational Physics, vol. VI, World Scientific, Dietrich Stauffer, 1998; see also http://arxiv.org/abs/quant-ph/9812037.
2. D.S. Abrams, C.P. Williams, Fast quantum algorithms for numerical integrals and stochastic processes, Technical report, 1999; see also http://arxiv.org/abs/quant-ph/9908083.
3. R. Beals, H. Buhrman, R. Cleve, M. Mosca, R. de Wolf, Quantum lower bounds by polynomials, in: Proceedings of 39th IEEE FOCS, 1998, pp. 352-361; see also http://arxiv.org/abs/quant-ph/9802049.
4. M. Boyer, P. Brassard, P. Høyer, A. Tapp, Tight bounds on quantum searching, Fortschritte Phys. 46 (1998) 493-505; see also http://arxiv.org/abs/quant-ph/9605034.
5. G. Brassard, P.Høyer, M. Mosca, A. Tapp, Quantum amplitude amplification and estimation, Technical report, 2000; see also http://arxiv.org/abs/quant-ph/0005055.
6. Deutsch D., Quantum theory, the Church-Turing principle and the universal quantum computer. Proc. R. Soc. London Ser. A. 400:1985;97-117.
7. A. Ekert, P. Hayden, H. Inamori, Basic concepts in quantum computation, 2000; see also http://arxiv.org/abs/quant-ph/0011013.
8. Feynman R., Simulating physics with computers. Int. J. Theor. Phys. 21:1982;467-488.
9. L. Grover, A fast quantum mechanical algorithm for database search, in: Proceedings of the 28th Annual ACM Symposium on the Theory of Computing, ACM Press, New York, 1996, pp. 212-219; see also http://arxiv.org/abs/quant-ph/9605043.
10. J. Gruska, Quantum Computing, McGraw-Hill, London, 1999.
11. S. Heinrich, Random approximation in numerical analysis, In: K.D. Bierstedt, A. Pietsch, W. M. Ruess, D. Vogt (Eds.), Functional Analysis, Marcel Dekker, New York, 1993, pp. 123-171.
12. S. Heinrich, Quantum summation with an application to integration, J. Complexity 18 (2002) 1-50; see also http://arxiv.org/abs/quant-ph/0105116.
13. S. Heinrich, Quantum integration in Sobolev classes, J. Complexity, 2002, in press; see also http://arxiv.org/abs/quant-ph/0112153.
14. S. Heinrich, E. Novak, Optimal summation and integration by deterministic, randomized, and quantum algorithms, In: K.-T. Fang, F.J. Hickernell, H. Niederreiter (Eds.), Monte Carlo and Quasi-Monte Carlo Methods 2000, Springer, Berlin, 2002, pp. 50-62; see also http://arxiv.org/abs/quant-ph/0105114.
15. S. Heinrich, E. Novak, On a problem in quantum summation. J. Complexity, 2002, in press; see also http://arxiv.org/abs/quant-ph/0109038.
16. Y.I. Manin, Computable and uncomputable, Sovetskoye Radio, Moscow, 1980 (in Russian).
17. Y.I. Manin, Classical computing, quantum computing, and Shor's factoring algorithm, 1999; see also http://arxiv.org/abs/quant-ph/9903008.
18. A. Nayak, F. Wu, The quantum query complexity of approximating the median and related statistics, STOC, May 1999, pp. 384-393; see also http://arxiv.org/abs/quant-ph/9804066.
19. M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, Cambridge, 2000.
20. E. Novak, Deterministic and stochastic error bounds in numerical analysis, Lecture Notes Math. 1349 (1988).
21. E. Novak, Quantum complexity of integration, J. Complexity 17 (2001) 2-16; see also http://arxiv.org/abs/quant-ph/0008124.
22. A.O. Pittenger, Introduction to Quantum Computing Algorithms, Birkhäuser, Boston, 1999.
23. Rabin M.O., Probabilistic algorithm for testing primality. J. Number Theor. 12:1980;128-138.
24. P.W. Shor, Algorithms for quantum computation: discrete logarithms and factoring, in: Proceedings of the 35th Annual Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1994, pp. 124-134; see also http://arxiv.org/abs/quant-ph/9508027.
25. P.W. Shor, Introduction to quantum algorithms, 2000; see also http://arxiv.org/abs/quant-ph/0005003.
26. Solovay R., Strassen V., A fast Monte Carlo test for primality. SIAM J. Comput. 6:1977;84-85.
27. J.F. Traub, H. Woźniakowski, Path integration on a quantum computer, 2001; see also http://arxiv.org/abs/quant-ph/0109113.
28. J.F. Traub, G.W. Wasilkowski, H. Woźniakowski, Information-Based Complexity, Academic Press, New York, 1988.